Details

analyze640.0ms (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.4s (16.6%)

Symmetry

(sort V l)

Results

955.0ms	8256×	body	128	valid
441.0ms	3997×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	15	12
3	15	12

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

20.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	20.4b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.1b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	6.2b	(/.f64 A (*.f64 V l))
✓	15.2b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series113.0ms (1.3%)

Counts

3 → 12

Calls

3 calls:

61.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
35.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
17.0ms	(/.f64 A (*.f64 V l))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`

Counts

3 → 72

Calls

3 calls:

6.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
3.0ms	(/.f64 A (*.f64 V l))
2.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

simplify96.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
679×	`associate-/r/_binary64`
449×	`div-sub_binary64`
262×	`times-frac_binary64`
261×	`sub-neg_binary64`

Counts

84 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	1084
1	194	1009
2	561	1009
3	1631	1009
4	2187	1009
5	2446	1009
6	3196	1009
7	4340	1009
8	4698	1009

prune93.0ms (1.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	17	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	17	87

Error

9.3b

Counts

87 → 17

Alt Table

Status	Error	Program
	41.9b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	20.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	41.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	20.8b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	39.0b	(.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))))
▶	19.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	43.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 A) V) (/.f64 (sqrt.f64 A) l))))
	22.8b	(.f64 c0 (exp.f64 (log.f64 (sqrt.f64 (/.f64 A (.f64 V l))))))
	20.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	21.0b	(.f64 (.f64 (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))))
	49.8b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V)) (sqrt.f64 (/.f64 (cbrt.f64 A) l))))
	20.8b	(.f64 c0 (.f64 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l))))))
	41.7b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	50.6b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	28.6b	(.f64 c0 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 A (.f64 V l))) 3)))
	44.9b	(exp.f64 (+.f64 (log.f64 c0) (log.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))))
	50.1b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 1 V)) (sqrt.f64 (/.f64 A l))))

Compiler

Compiled 1776 to 659 computations (62.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.1b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
✓	5.7b	(*.f64 (/.f64 1 V) (/.f64 A l))
✓	15.2b	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

series125.0ms (1.4%)

Counts

3 → 48

Calls

3 calls:

64.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
35.0ms	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))
25.0ms	(*.f64 (/.f64 1 V) (/.f64 A l))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`add-exp-log_binary64`
25×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

3 → 98

Calls

3 calls:

10.0ms	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))
8.0ms	(*.f64 (/.f64 1 V) (/.f64 A l))
7.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))

simplify149.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

474×	`sqr-pow_binary64`
426×	`associate-*l/_binary64`
402×	`fabs-mul_binary64`
354×	`associate-/l*_binary64`
346×	`associate-*r/_binary64`

Counts

146 → 159

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	146	1670
1	321	1517
2	962	1517
3	2549	1517
4	2665	1517
5	3041	1517
6	3415	1517
7	4032	1517
8	4825	1517
9	5183	1517

prune144.0ms (1.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	155	4	159
Fresh	7	9	16
Picked	0	1	1
Done	0	0	0
Total	162	14	176

Error

5.4b

Counts

176 → 14

Alt Table

Status	Error	Program
	24.3b	(.f64 c0 (/.f64 (sqrt.f64 (.f64 (/.f64 1 V) A)) (sqrt.f64 l)))
	49.8b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V)) (sqrt.f64 (/.f64 (cbrt.f64 A) l))))
	41.9b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	20.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	41.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	20.8b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	39.0b	(.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))))
✓	19.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	22.3b	(.f64 c0 (exp.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))))
	41.7b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	50.6b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
▶	20.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))
	20.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	25.8b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))

Compiler

Compiled 2986 to 1428 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))
✓	2.4b	(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))
	5.7b	(*.f64 (/.f64 1 V) (/.f64 A l))
	15.2b	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

series718.0ms (8.3%)

Counts

2 → 36

Calls

2 calls:

648.0ms	(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))
70.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))

rewrite77.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`sqrt-div_binary64`
24×	`associate-*r/_binary64`
18×	`frac-times_binary64`
12×	`associate-*l/_binary64`
11×	`pow1_binary64`

Counts

2 → 61

Calls

2 calls:

16.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))
5.0ms	(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))

simplify117.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

509×	`unswap-sqr_binary64`
460×	`fma-neg_binary64`
389×	`fma-def_binary64`
254×	`sqr-pow_binary64`
241×	`div-sub_binary64`

Counts

97 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	1689
1	292	1573
2	633	1573
3	984	1429
4	1461	1429
5	2823	1429
6	4628	1429
7	4956	1429

prune369.0ms (4.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	374	3	377
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	376	15	391

Error

5.4b

Counts

391 → 15

Alt Table

Status	Error	Program
	24.3b	(.f64 c0 (/.f64 (sqrt.f64 (.f64 (/.f64 1 V) A)) (sqrt.f64 l)))
	49.8b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V)) (sqrt.f64 (/.f64 (cbrt.f64 A) l))))
	22.3b	(.f64 c0 (exp.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))))
▶	20.5b	(.f64 (.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))))
	20.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	41.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	26.0b	(/.f64 (.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) A)))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) A)))) (*.f64 (sqrt.f64 (sqrt.f64 l)) (sqrt.f64 (sqrt.f64 l))))
	41.7b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	20.8b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
✓	19.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	50.6b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	31.3b	(.f64 (.f64 c0 (sqrt.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 A (.f64 V l))) 3)))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))
✓	20.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))
	20.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	25.8b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))

Compiler

Compiled 10438 to 5376 computations (48.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))))
	2.4b	(sqrt.f64 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l))))
	5.7b	(*.f64 (/.f64 1 V) (/.f64 A l))
	15.2b	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

series547.0ms (6.3%)

Counts

1 → 24

Calls

1 calls:

546.0ms

(cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cbrt-prod_binary64`
6×	`sqrt-div_binary64`
5×	`sqrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 20

Calls

1 calls:

5.0ms

(cbrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
642×	`unswap-sqr_binary64`
529×	`fma-neg_binary64`
243×	`div-sub_binary64`
235×	`fma-def_binary64`

Counts

44 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	766
1	140	766
2	232	766
3	507	622
4	849	622
5	1886	622
6	4837	622
7	5145	622

prune892.0ms (10.3%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	752	0	752
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	752	15	767

Error

5.4b

Counts

767 → 15

Alt Table

Status	Error	Program
	24.3b	(.f64 c0 (/.f64 (sqrt.f64 (.f64 (/.f64 1 V) A)) (sqrt.f64 l)))
	49.8b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V)) (sqrt.f64 (/.f64 (cbrt.f64 A) l))))
	22.3b	(.f64 c0 (exp.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))))
✓	20.5b	(.f64 (.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))))
	20.5b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
	41.0b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	26.0b	(/.f64 (.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) A)))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) A)))) (*.f64 (sqrt.f64 (sqrt.f64 l)) (sqrt.f64 (sqrt.f64 l))))
	41.7b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	20.8b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
✓	19.9b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	50.6b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	31.3b	(.f64 (.f64 c0 (sqrt.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 A (.f64 V l))) 3)))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))
✓	20.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l)))))
	20.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	25.8b	(/.f64 (*.f64 c0 (sqrt.f64 (/.f64 A V))) (sqrt.f64 l))

Compiler

Compiled 37520 to 21325 computations (43.2% saved)

regimes2.6s (30%)

Accuracy

Total 3.7b remaining (40.9%)

Threshold costs 0b (0%)

Counts

130 → 5

Compiler

Compiled 26398 to 17056 computations (35.4% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	122
1	50	122
2	49	122

end346.0ms (4%)

Compiler: Compiled 633 to 380 computations (40% saved)

Details

analyze640.0ms (7.4%)

sample1.4s (16.6%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series113.0ms (1.3%)

rewrite16.0ms (0.2%)

simplify96.0ms (1.1%)

prune93.0ms (1.1%)

localize9.0ms (0.1%)

series125.0ms (1.4%)

rewrite35.0ms (0.4%)

simplify149.0ms (1.7%)

prune144.0ms (1.7%)

localize9.0ms (0.1%)

series718.0ms (8.3%)

rewrite77.0ms (0.9%)

simplify117.0ms (1.3%)

prune369.0ms (4.3%)

localize13.0ms (0.2%)

series547.0ms (6.3%)

rewrite8.0ms (0.1%)

simplify74.0ms (0.9%)

prune892.0ms (10.3%)

regimes2.6s (30%)

bsearch4.0ms (0.1%)

simplify4.0ms (0%)

end346.0ms (4%)

Profiling